A general theory of arbitrary Bessel beam scattering and interactions with a sphere.

This paper presents an analytical theory that formulates interactions of an arbitrary-order Bessel beam with an arbitrarily located sphere as a superposition of interactions with a series of Bessel beams of different orders whose axis is through the object's center. The analysis is via a parallel-axis relation that is derived to represent the incident Bessel beam as a superposition of a series of Bessel beams of different orders along a parallel, shifted axis. By the superposition, summing on-axial formulas gives off-axial formulas, including multipole expansion of the incident beam, scattered fields, powers of scattering and absorption, and axial radiation forces. Features of the off-axial scattering and interactions are hence accessed from prior studies on the axially centered illuminations. Dependence on the object location is contained in a weighting function in the superposition that also depends on the beam orders. Transverse and azimuthal forces are interpreted as a result of interactions between the beams of different orders in the superposition.